Square Root Calculator › Square root of 60
Square Root of 60
√60 ≈ 7.745967
60 is not a perfect square, so √60 is an irrational number that is approximately 7.745967. In simplified radical form, √60 = 2√15.
√60 lies between √49 = 7 and √64 = 8.
| Number | 60 |
| Square root (decimal) | 7.745967 |
| Simplified radical | 2√15 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 60
60 = 2^2 × 3 × 5. This is what determines the simplified radical: for √60 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √60 = 2√15.
Estimating √60 by hand
√60 falls between √49 = 7 and √64 = 8, so it starts at 7.something. The Babylonian method refines that guess by averaging it with 60 ÷ the guess:
| Step | Estimate |
| Start | 7 |
| Step 1 | 7.785714 |
| Step 2 | 7.746068 |
| Step 3 | 7.745967 |
After 3 steps the estimate is 7.745967, matching √60 ≈ 7.745967.
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Frequently asked questions
Is 60 a perfect square?
No, 60 is not a perfect square, so its square root is irrational and approximately 7.745967.
What is the square root of 60 in simplest radical form?
√60 = 2√15 in simplest radical form.